`1- Liz saved $270 at the end of every month for 6 years in her bank...

`1-

Liz saved $270 at the end of every month for 6 years in her bank account that earned 3.70% compounded monthly.

a. What is the accumulated value of her savings at the end of the period?

a$21,393.49

b$21,729.45

c$196,528.63

d$2,289.45

b. What is the interest earned over the period?

a$2,019.45

b$21,729.45

c$2,559.45

d$2,289.45

What nominal interest rate compounded semi-annually is equivalent to 3.63% compounded quarterly?

3-If Lionel wants to earn interest of $3,547.75 on his $11,000.00 savings in 2 years, at what nominal interest rate compounded quarterly do you suggest he invests his money?

4-Orange Company holds a loan with an interest rate of 6.00% compounded quarterly. Calculate the effective rate of the loan.

Solutions

Expert Solution

Answer to Question 1:

Monthly Deposit = $270
Time Period = 6 years or 72 months

Annual Interest Rate = 3.70%
Monthly Interest Rate = 3.70% / 12
Monthly Interest Rate = 0.30833%

Accumulated Sum = $270*1.0030833^71 + $270*1.0030833^70 + … + $270*1.0030833 + $270
Accumulated Sum = $270 * (1.0030833^72 - 1) / 0.0030833
Accumulated Sum = $270 * 80.479362
Accumulated Sum = $21,729.45

Total Deposit = 72 * $270.00
Total Deposit = $19,440.00

Total Interest Earned = Accumulated Sum - Total Deposit
Total Interest Earned = $21,729.45 - $19,440.00
Total Interest Earned = $2,289.45

Answer to Question 2:

Annual Interest Rate = 3.63% compounded quarterly

Quarterly Interest Rate = 3.63% / 4
Quarterly Interest Rate = 0.9075%

Effective Annual Rate = (1 + Quarterly Interest Rate)^4 - 1
Effective Annual Rate = (1 + 0.009075)^4 - 1
Effective Annual Rate = 1.036797 - 1
Effective Annual Rate = 0.036797 or 3.6797%

Semiannual Interest Rate = (1 + Effective Annual Rate)^(1/2) - 1
Semiannual Interest Rate = (1 + 0.036797)^(1/2) - 1
Semiannual Interest Rate = 1.018232 - 1
Semiannual Interest Rate = 0.018232 or 1.8232%

Nominal Interest Rate compounded semiannually = 2 * Semiannual Interest Rate
Nominal Interest Rate compounded semiannually = 2 * 1.8232%
Nominal Interest Rate compounded semiannually = 3.6464% or 3.65%

jeff jeffy answered 1 year ago

Next > < Previous

Related Solutions

Jack has saved $225 at the end of every month in his bankaccount for 6...

Jack has saved $225 at the end of every month in his bank account for 6 years with the rate of interest being 3.6% p.a. compounding monthly, then he decided to go to school for 5 years when he could not contribute to his account. After his studies ended (at the end of the 5th year at school), he moved his balance to another account and started to withdraw equal amounts of money from his account at the end of...

Jack has saved $225 at the end of every month in his bankaccount for 6...

Lionel deposited $1,500 at the end of every month into an RRSP for 6 years. The...

Lionel deposited $1,500 at the end of every month into an RRSP for 6 years. The interest rate earned was 3.75% compounded semi-annually for the first 3 years and changed to 4.00% compounded monthly for the next 3 years. What was the accumulated value of the RRSP at the end of 6 years? Round to the nearest cent

1. Lucy deposited $1,300 at the end of every month into an RRSP for 9 years....

1. Lucy deposited $1,300 at the end of every month into an RRSP for 9 years. The interest rate earned was 4.50% compounded semi-annually for the first 3 years and changed to 4.75% compounded monthly for the next 6 years. What was the accumulated value of the RRSP at the end of 9 years? ( pls give me solution too ) 2. While buying a new car, Helen made a down payment of $1,100.00 and agreed to make month-end payments...

Suppose you saved $483 at the end of each month for 37 years and your savings...

Suppose you saved $483 at the end of each month for 37 years and your savings earned an interest rate of 3.5%. If instead you had saved for only 11 years, how much would you have had to save each month in order to reach the same final balance? Round to the nearest cent.

If Haley invests $1,000 at the end of every month (EOM) for seven years in an...

If Haley invests $1,000 at the end of every month (EOM) for seven years in an investment paying an annual rate of 10% compounded monthly, how much will she have at the end of seven years? If Haley invests $1,000 at the beginning of every month (BOM) for seven years in an investment paying an annual rate of 10% compounded monthly, how much will she have at the end of seven years?

Candice deposits into her savings account at the end of every month. During the first year,...

Candice deposits into her savings account at the end of every month. During the first year, she deposits 10 each month. During the second year, Candice deposits 20 each month. During the third year, the deposits are 30. The pattern continues, concluding with deposits of 160 per month during the 16th year. Candice earns an annual nominal interest rate of 12% compounded monthly. How much will Candice have accumulated after 16 years?

You’re prepared to make monthly payments of $270, beginning at the end of this month, into...

You’re prepared to make monthly payments of $270, beginning at the end of this month, into an account that pays 6.8 percent interest compounded monthly. How many payments will you have made when your account balance reaches $18,000? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

1.Mr. Clark made deposits of $950 at the end of every 6 months for 15 years....

1.Mr. Clark made deposits of $950 at the end of every 6 months for 15 years. If interest is 3% compounded monthly and if he leaves the accumulated balance for another 10 years, what will be the balance in his account then? (i.e. 10 years after the last deposit) _______________ How much of the accumulated amount is interest? 2.Amy borrowed $6,200 to buy a car to drive to school. She plans to study for three years, and then start her...

If you invest $8,717.24 at the end of every month for the next 8 years, what...

If you invest $8,717.24 at the end of every month for the next 8 years, what will be you account balance immediately after the last payment is deposited? The interest rate you will earn on the account is 15.75%

Subjects